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A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves

Year 2020, , 78 - 90, 20.03.2020
https://doi.org/10.36753/mathenot.656850

Abstract

We classify the curvature of interpolating sesqui-harmonic Legendre curves in generalized Sasakian space forms. We investigate the necessary and sufficient conditions for these types of curves in nine cases to be interpolating sesqui-harmonic.

References

  • Alegre, P., Blair, D.E., Carriazo, A., Generalized Sasakian space forms, Israel J. of Math., 141, 157-183 (2004).
  • Alegre, P., Carriazo, A., Structures on generalized Sasakian space forms, Differ. Geom. Appl., 26(6), 656-666 (2008)
  • Blair, DE., Riemannian Geometry of Contact and Symplectic Manifolds, Boston, Birkhauser, (2002).
  • Blair, D.E., The theory of quasi-Sasakian structures, J. Differ. Geom., 1, 331-345 (1967)
  • Branding, V., On interpolating sesqui-harmonic maps between Riemannian manifolds, J. Geom. Anal. (2019).
  • Branding, V., Some analytic results on interpolating sesqui-harmonic maps, arXiv preprint arXiv:1907.04167 (2019).
  • Eells, J. Jr., Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86: 109-160 (1964).
  • Jiang, GY., 2-Harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A, 7, 389-402 (1986).
  • Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, 93-103 (1972).
  • Karaca, F., Ozgür, C., De, U. C., On Interpolating Sesqui-Harmonic Legendre Curves inSasakian Space Forms, International Journal of Geometric Methods in Modern Physics, in press (2019).
  • Laugwitz, D., Differential and Riemannian geometry, New York-London, (1965).
  • Loubeau, L., Montaldo, S., Biminimal immersions, Proc. Edinb. Math. Soc., 51, 421-437 (2008).
  • Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Dif. Geo., 4, 237-244 (1970).
  • Marrero, J.C., The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl., 162, 77-86 (1992).
  • Oubina, J.A., New classes of almost contact metric structures, Publ. Math. Debrecen, 32(3-4), 187-193 (1985).
  • Ozgür, C., Güvenç, Ş., On some classes of biharmonic Legendre curves in generalized Sasakian space forms, Collect. Math., 65(2), 203-218 (2014).
Year 2020, , 78 - 90, 20.03.2020
https://doi.org/10.36753/mathenot.656850

Abstract

References

  • Alegre, P., Blair, D.E., Carriazo, A., Generalized Sasakian space forms, Israel J. of Math., 141, 157-183 (2004).
  • Alegre, P., Carriazo, A., Structures on generalized Sasakian space forms, Differ. Geom. Appl., 26(6), 656-666 (2008)
  • Blair, DE., Riemannian Geometry of Contact and Symplectic Manifolds, Boston, Birkhauser, (2002).
  • Blair, D.E., The theory of quasi-Sasakian structures, J. Differ. Geom., 1, 331-345 (1967)
  • Branding, V., On interpolating sesqui-harmonic maps between Riemannian manifolds, J. Geom. Anal. (2019).
  • Branding, V., Some analytic results on interpolating sesqui-harmonic maps, arXiv preprint arXiv:1907.04167 (2019).
  • Eells, J. Jr., Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86: 109-160 (1964).
  • Jiang, GY., 2-Harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A, 7, 389-402 (1986).
  • Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, 93-103 (1972).
  • Karaca, F., Ozgür, C., De, U. C., On Interpolating Sesqui-Harmonic Legendre Curves inSasakian Space Forms, International Journal of Geometric Methods in Modern Physics, in press (2019).
  • Laugwitz, D., Differential and Riemannian geometry, New York-London, (1965).
  • Loubeau, L., Montaldo, S., Biminimal immersions, Proc. Edinb. Math. Soc., 51, 421-437 (2008).
  • Ludden, G.D., Submanifolds of cosymplectic manifolds, J. Dif. Geo., 4, 237-244 (1970).
  • Marrero, J.C., The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl., 162, 77-86 (1992).
  • Oubina, J.A., New classes of almost contact metric structures, Publ. Math. Debrecen, 32(3-4), 187-193 (1985).
  • Ozgür, C., Güvenç, Ş., On some classes of biharmonic Legendre curves in generalized Sasakian space forms, Collect. Math., 65(2), 203-218 (2014).
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Fatma Karaca 0000-0002-0382-8028

Publication Date March 20, 2020
Submission Date December 8, 2019
Acceptance Date February 14, 2020
Published in Issue Year 2020

Cite

APA Karaca, F. (2020). A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves. Mathematical Sciences and Applications E-Notes, 8(1), 78-90. https://doi.org/10.36753/mathenot.656850
AMA Karaca F. A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves. Math. Sci. Appl. E-Notes. March 2020;8(1):78-90. doi:10.36753/mathenot.656850
Chicago Karaca, Fatma. “A Note on Generalized Sasakian Space Forms With Interpolating Sesqui-Harmonic Legendre Curves”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 78-90. https://doi.org/10.36753/mathenot.656850.
EndNote Karaca F (March 1, 2020) A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves. Mathematical Sciences and Applications E-Notes 8 1 78–90.
IEEE F. Karaca, “A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 78–90, 2020, doi: 10.36753/mathenot.656850.
ISNAD Karaca, Fatma. “A Note on Generalized Sasakian Space Forms With Interpolating Sesqui-Harmonic Legendre Curves”. Mathematical Sciences and Applications E-Notes 8/1 (March 2020), 78-90. https://doi.org/10.36753/mathenot.656850.
JAMA Karaca F. A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves. Math. Sci. Appl. E-Notes. 2020;8:78–90.
MLA Karaca, Fatma. “A Note on Generalized Sasakian Space Forms With Interpolating Sesqui-Harmonic Legendre Curves”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 78-90, doi:10.36753/mathenot.656850.
Vancouver Karaca F. A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves. Math. Sci. Appl. E-Notes. 2020;8(1):78-90.

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